The concept of Granger-Causality (GC) is widely used to draw inference concerning causality in applied economics. Stationary series are the term of reference used in GC testing, which is generally studied by means of a standard Dickey-Fuller test. We prove that, when the Data Generating Process (DGP) of the variables is either Broken-Trend Stationary (BTS) or Broken-Mean Stationary (BMS), correct inference can not be drawn from a standard Granger-Causality test and may identify inexistent causal relationships, even if the former variables are differenced. Asymptotic and finite-sample evidence in this sense is provided.